Jake's car needs repairs but he is short of cash. A payday loan company charges a fee of 46 for a two week loan of 250. This is equivalent to a discounted loan with proceeds of 250 and a loan amount of 296. What is the per annum interest rate?

296 = 250 [1 + (I/100)/26]

where I is the interest rate in %

296/250 = 1.184 = [1 + (I/100)*(1/26)]

I/2600 = 0.184

I = 478%

To calculate the per annum interest rate, we need to first determine the total interest charged for the two-week loan. From the given information, we know that the fee charged by the payday loan company is $46 for a $250 loan.

To find the total interest charged, we need to subtract the loan amount (proceeds) from the loan amount including the fee. In this case, the loan amount including the fee is $296 ($250 + $46).

Therefore, the total interest charged for the two-week loan is $296 - $250 = $46.

Now, since the annual interest rate is typically expressed as a percentage, we need to convert the two-week interest into an annual rate.

There are 52 weeks in a year, so if we assume that the interest charged for a two-week loan would be incurred every two weeks over a year, we can multiply the total interest charged by 26 to get an estimate of the annual interest.

$46 x 26 = $1,196.

Therefore, the estimated annual interest for this loan is $1,196.

To get the per annum interest rate, we need to calculate the percentage of the loan amount ($250) that the annual interest ($1,196) represents.

Per annum interest rate formula:
Per Annum Interest Rate = (Annual Interest / Loan Amount) x 100

Per Annum Interest Rate = ($1,196 / $250) x 100

Per Annum Interest Rate = 478.4%.

So, the per annum interest rate for this payday loan is approximately 478.4%.